In a large pot, heat vegetable oil over medium heat.
Add diced onion and cook, stirring occasionally, until the onion is soft and translucent.
Stir in the minced garlic and cook for about 1 minute, just until fragrant.
Add chicken broth, shredded chicken, tomatoes, corn, beans, buffalo sauce, and salsa verde. Stir everything together.
Bring the soup to a simmer. Let it cook for about 15 minutes, stirring occasionally.
Lower the heat to low. Add cream cheese and shredded cheddar cheese. Stir often until the cheese is completely melted and the soup is smooth.
Season with kosher salt and ground black pepper to taste.
Serve hot, topped with green onion, sour cream, chopped cilantro, and a drizzle of buffalo sauce, if desired.